I have a question about this problem.

If f(x,y,z) = 0 and g(x,y,z) = 0, show that these three fractions are equal:

I know dF and dG both equal zero, but setting them both equal to zero and using Jacobians does not get me to the final answer. I don't know what else to try. Any help would be greatly appreciated!

Here is a better version!